Two parameters control the Introduction and Withdrawal procedure. The ToRecruitingProc parameter defines what part of population (from 0 to 1) will be subjected to the procedure. Another parameter, moreover WithdrAdd (from 0 to 1) specifies the probability that a given solution (W matrix) will be subjected to Gene Withdrawal or Gene Introduction. (If WithdrAdd = 0 then all solutions will go through Gene Introduction only; If WithdrAdd = 1 then all solutions will go through Gene Withdrawal only.)Figure 4Gene Introduction adds a new (n + 1) column (right-most) and row (lowest) to the W interaction matrix. Gene Withdrawal eliminates the right-most column and bottom row.2.3.2.

Involvement of the Recruited Gene in the Functioning of the GRN To quantify how much added genes affect network fitness, we used the following procedure: the model solution in a given generation was evaluated according to (2); then, for each additional gene (above the obligatory 2), fit to the data was evaluated with the W elements for that gene zeroed out. In cases where this produced a drop in fitness score (2) of more than 10% (a threshold determined in preliminary runs) compared to the full GRN, we kept the added genes as recruits to the GRN. We further filtered the most functionally significant recruits by use of a 33% threshold. Results are presented below for both threshold levels.2.3.3. Evaluation of GRN Robustness GRN solutions with E scores below threshold represent good fits to the gene expression data (Figure 3(a)). That is, these GRNs solve the problem of forming gap expression domains.

In addition to this, though, we want to test the robustness of these gap solutions to maternal variability. To do this, we took each good solution and tested its robustness to Bcd variability. We perturbed Bcd from Figure 3(b) according to[bcd]=[bcd]��[bcd]?Random?(0.2)?(3)(i.e., Brefeldin_A the Bcd profile varied within limits of ��20%). We reran the GRN with the perturbed Bcd values and compared these against the unperturbed result according toE��=��b(viaperturbed?viaunperturb)2.(4)This measure was calculated for 100Bcd perturbations for each GRN, and the results averaged for a measure of the GRN’s robustness (e.g., Figure 12).Figure 122-gradient model (Bcd-Cad) shows robustness to Bcd variability. Bcd��green; Kr��red; kni��blue. (a) Highly robust Kr and kni. (b) Nonrobust Kr and kni. (c) All borders are robust, except for anterior Kr. (d) Severe nonrobustness, …2.3.4. Artificial Transposons for GA The above Gene Introduction operator does not model the mechanism by which genes are incorporated into the genome.